1. Field of the Invention
The present invention relates to helical and circular x-ray computed tomographic (CT) imaging, and in particular to CT imaging with circular reconstruction with extended volume coverage and improved dose utilization.
2. Discussion of the Background
For computed tomography (CT), there are two main types of detectors: curved and flat, as shown in FIGS. 1A and 1B, respectively. The curved detector represents a cylindrical surface parallel to the z-axis (axis of rotation) and focused on the ray source. The flat detector represents a flat surface parallel to the z-axis. Even though detectors are physically placed at some distance D from the source, it is a common approach to consider a detector at distance R (radius of the source trajectory) from the source, so that detector contains the rotation axis.
The most commonly used reconstruction algorithm for circular cone beam CT is proposed in L. A. Feldkamp, L. C. Davis and J. W. Kress, “Practical cone beam algorithm,” Journal of Optical Society of America, vol. 1 (6), pp. 612-619 (1984), hereinafter FDK. The algorithm uses full rotation of data, also called full scan (FS). Parker proposed a method where only π+FA, where FA is the Full detector fan angle opening. These parameters are not defined yet) of data angular range is used. D. Parker, “Optimal short scan convolution reconstruction for fan-beam CT,” Med. Phys., vol. 9, pp. 254-257 (1982).
The reconstruction volume for FS will be described with reference to FIGS. 2A and 2B. The field-of-view (FOV) 20 with a reconstruction pixel 21 at a distance r from the center of the FOV is scanned with x-rays at source to center distance R. The volume reconstruction region with circular scanning is limited in the z-direction by the divergent x-ray beam. A divergent x-ray beam does not cover the full z-extent of the FOV 20 on the source side, so that some corner parts of the FOV are not exposed at a particular view angle (see FIG. 2B). Thus, z-coverage is maximum at the center, and reduces at periphery, so that the reconstruction FOV has a hexagonal shape, illustrated by region 22 with the heavier lines in FIG. 2B. However, because the x-ray source rotates, the missing parts are covered by the x-ray beam when the source is on the opposite side.
The volume z-coverage at the distance r from the center is given by
                                          H            FS                    ⁡                      (            r            )                          =                  W          ⁢                                    R              -              r                        R                                              (        1        )            
W is the detector half-width at center. At the center (r=0) maximum z-coverage is obtained, with H=W. Moving away from the center, z-coverage linearly reduces. Note that in the case of the full scan, z-coverage is independent of detector type, i.e., flat or curved. A reconstruction pixel has polar coordinates (r, φ). Its short scan reconstruction range, denoted [βstart, βend], is shown in FIG. 2C. FIG. 2D shows the z-coverage, where H(r) is the half-height of the volume z-coverage at the distance r from the center. The fan angle under which the reconstruction pixel is viewed from boundary views (βstart, βend) is given by:
                              γ          ⁡                      (            r            )                          =                  arcsin          ⁡                      (                          r              R                        )                                              (        2        )            
View-range endpoints are given by:βstart(r,φ)=φ+π−Δβ(r)/2βend(r,φ)=φ+π+Δβ(r)/2=βstart(r,φ)+Δβ(r)  (3)
where Δβ(r) is the reconstruction view-range and is given by:Δβ(r)=π+2γ(r)  (4)
The volume z-coverage at the distance r from the center in case of short scan with curved detector is given by:
                                          H                          SS              -              CD                                ⁡                      (            r            )                          =                              W            ⁢                          d              R                                =                                    W              ⁢                                                          ⁢              cos              ⁢                                                          ⁢                              γ                ⁡                                  (                  r                  )                                                      =                          W              ⁢                                                                                          R                      2                                        -                                          r                      2                                                                      R                                                                        (        5        )            
The volume z-coverage at the distance r from the center in case of short scan with flat detector is given by:
                                          H                          SS              -              FD                                ⁡                      (            r            )                          =                              W            ⁢                          d                                                R                  /                  cos                                ⁢                                                                  ⁢                                  γ                  ⁡                                      (                    r                    )                                                                                =                                    W              ⁢                                                          ⁢                              cos                2                            ⁢                                                          ⁢                              γ                ⁡                                  (                  r                  )                                                      =                          W              ⁢                                                                                          R                      2                                        -                                          r                      2                                                                            R                    2                                                  .                                                                        (        6        )            
Volume z-coverage with different scans as a function of r is shown in FIG. 2E. Coverage for full scan (23), short scan with flat detector (24) and short scan with curved detector (25) are shown. For these curves, W=80 mm, and R=600 mm. Short scan provides much better z-coverage compared to the full scan, and the curved detector provides better coverage than the flat detector.